ICSE Class 10 Ratio and Proportion — Mock Test (2027)

Free online mock test for Ratio and Proportion (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.If $x = \frac{\sqrt{2a + 3b} + \sqrt{2a - 3b}}{\sqrt{2a + 3b} - \sqrt{2a - 3b}}$, which of the following equations is satisfied by $x$?
   • A.$3bx^2 - 4ax + 3b = 0$
   • B.$3bx^2 + 4ax + 3b = 0$
   • C.$3bx^2 - 4ax - 3b = 0$
   • D.$4bx^2 - 3ax + 4b = 0$
2. 2.If 6 is the mean proportion between two numbers x and y, and 48 is the third proportional to x and y, what are the values of x and y?
   • A.x = 2, y = 18
   • B.x = 3, y = 12
   • C.x = 4, y = 9
   • D.x = 6, y = 6
3. 3.The ages of Shruti and Divya are in the ratio 5:7. Five years hence, their ages will be in the ratio 3:4. What are their present ages?
   • A.Shruti is 20 years and Divya is 28 years
   • B.Shruti is 25 years and Divya is 35 years
   • C.Shruti is 15 years and Divya is 21 years
   • D.Shruti is 30 years and Divya is 42 years
4. 4.Solve the equation $\frac{1 - px}{1 + px} \sqrt{\frac{1 + qx}{1 - qx}} = 1$ for $x$ using properties of proportion. What is the non-zero solution?
   • A.$x = \pm \frac{1}{p} \sqrt{\frac{2p - q}{q}}$
   • B.$x = \pm \frac{1}{q} \sqrt{\frac{2p - q}{p}}$
   • C.$x = \pm \frac{1}{p} \sqrt{\frac{p - q}{q}}$
   • D.$x = \pm \frac{1}{q} \sqrt{\frac{p + q}{p}}$
5. 5.If $x = \frac{\sqrt{3a + 2b} + \sqrt{3a - 2b}}{\sqrt{3a + 2b} - \sqrt{3a - 2b}}$, which of the following equations can be proven to hold true for $x$?
   • A.$bx^2 - 3ax + b = 0$
   • B.$bx^2 + 3ax + b = 0$
   • C.$3ax^2 - bx + 3a = 0$
   • D.$2bx^2 - 3ax + 2b = 0$